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Expectation And Hourly RateThe Fundamental Theorem Of PokerThe Ante StructurePot OddsEffective OddsImplied Odds and Reverse Implied OddsThe Value of DeceptionWin the Big Pots Right AwayThe Free CardThe Semi-BluffDefense Against the Semi-BluffRaising
Check-RaisingSlowplayingLoose and Tight PlayPositionBluffingGame Theory and BluffingInducing and Stopping BluffsHands-Up On The EndReading HandsThe Psychology of PokerAnalysis at the TableEvaluating the Game


  When there is only one round of betting left and only one card to come, comparing your chances of improving to the   pot odds you are getting is a relatively straightforward proposition.

  If your chances of making a hand you know will win are, say, 4-to-1 against and you must call a $20 bet for the   chance to win a $120 pot, then clearly your hand is worth a call because you’re getting 6-to-1 odds the pot is offering   you (excluding bets on the end) are greater than the 4-to-1 odds against you  making your online poker hand.

  However, when there is more than one card to come, you must be very careful in determining your real pot odds.

  Many players make a classic mistake: They know their chances of improving, let’s say, with three cards to come, they   compare those chances to the pot odds they are getting right now.

  But such a comparison is completely off the mark since the players are going to have to put more money into the pot   in future betting rounds, and they must take that money into account.

  It’s true that the chances of making a hand improve greatly when there are two or three cards to come, but the odds   you are getting from the pot worsen.


  Let’s say you are playing hold’em, and after the flop you have a four-flush that you are sure will win if you hit if. There   are two cards to come, which improves your odds of making the flush to approximately 1¾-to-1.

  It is a $10-$20 game with $20 in the pot, and your single opponent has bet $10. You may say, “I’m getting 3-to-1 odds   and my chances are 1¾-to-1.

  So I should call.” However, the 1¾-to-1 odds of making the flush apply only if you intend to see not just the next card,   but the last card as well, and to see the last card you will probably have to call not just $10 now but also $20 on the   next round of betting.

  Therefore, when you decide you’re going to see a hand that needs improvement all the way through to the end, you   can’t say you are getting, as in this case, 30-to-10 odds.

  You have to say, “Well, if I miss my hand, I lose $10 on this round of betting and $20 on the next round. In all, I lose   $30.

  If I make my hand, I will win the $30 in there now plus $20 on the next round for a total of $50.” All of a sudden,   instead of 30-to-10, you’re getting only 50-to-30 odds, which reduces to 1²∕³-to-1.

  These are your effective odds the real odds you are getting from the pot when you call a bet with more than one   card to come.

  Since you are getting only 1²∕³-to-1 by calling a $10 bet after the flop, and your chances of making the flush are   1¾-to-1, you would have to throw away the hand, because it has turned into a losing play that is, a play with   negative expectations.

  The only time it would be correct to play the hand in this situation is if you could count on your opponent to call a bet   at the end, after your flush card hits.

  Then your potential $50 win increases to $70, giving you 70-to-30 odds an justifying a call.(* While a call on the flop   might be a bad play, a semi-bluff raise could be a good play. Sometimes folding is a better alternative to calling, but   raising is the best alternative of all. (See Chapter Eleven and Thirteen.) back-door flush draw in hold’em, and an   opponent bets $10.)

  With a back-door flush you need two in a row of a suit. To make things simple, we’ll assume the chances of catching   two consecutive of a particular suit are 1/5 X 1/5.

  That’s not quite right, but it’s close enough.³ It means you’ll hit a flush once in 25 tries on average, making you a
  24-to-1 underdog.(*For the finicky, the exact equation is 10/47 x 9/46. Ten of the 47 unseen cards make a four-flush   on fourth street, and then nine of the 46 remaining cards will produce the flush at the end.)

  By calling your opponent’s $10 bet, you would appear to be getting 26-to-1. So you might say, “OK, I’m getting
  26-to-1, and it’s only 24-to-1 against me. Therefore, I should call to try to make my flush.”

  Your calculations are incorrect because they do not take into account your effective odds. One out of 25 times you will   win the $260 in there, plus probably another $40 on the last two rounds of betting.

  Twenty times you will lose only $10 when your first card does not hit, and you need not call another bet. But the   remaining four times you will lose a total of $30 each time when your first card hits, you call your opponent’s $20 bet,   and your second card does not hit.

  Thus, after 25 such hands, you figure to lose $320 ($200+$120) while winning $300 for a net loss of $20. Your   effective poker odds reveal a call on the flop to be a play with negative expectation and hence incorrect.

Situations When Effective Odds Need Not Apply